EN 206 - Power Electronics and Machines

EN 206 - Power Electronics and MachinesInduction Motor

Suryanarayana DoollaDepartment of Energy Science and Engineering

Indian Institute of Technology, [email protected]

07 March 2011

Prof. Doolla () EN 206 1/16 07 March 2011 1 / 16

Lecture Organization - Modules

Introduction and Power Semiconductor Switches

Module 1: Transformers

Module 2: AC/DC converter / Rectifier

Module 3: DC machines and Drives

Module 4: DC/DC converter

Module 5: Induction Machine

Module 6: DC/AC converter / Inverter

Module 7: AC/AC converter / Cyclo converter

Module 8: Synchronous Machine

Module 9: Special Topics: Machines, HVDC, APF

basic principle

Rotating Magnetic Field

When balanced polyphase currents flow in a balanced polyphasewindings, a rotating magnetic field is produced.

For a 3 phase machine, the three windings are displaced from eachother by 120o electrical space degrees along the air-gap periphery.

Production of rotating magnetic field can be verified both bygraphical and mathematical analysis.

basic principle

Three phase winding space distributed by 120o electrical, Three coilsrepresent three phase winding and Three phase instantaneous currents

basic principle

State-1

Ia = Im; Ib = −Im/2; Ic = −Im/2The maximum mmf set by thecurrent is Fm,The resultant mmf Fr is given byFr = Fm + 2Fmcos(60)

2 directedalong ‘a’ axis

State-2

Ia = −Im/2; Ib = −Im/2; Ic = ImThe resultant mmf Fr is given byFr = Fm + 2Fmcos(60)

2 directedalong ‘c’ axis

basic principle

State-3

Ia = −Im/2; Ib = Im; Ic = −Im/2The resultant mmf Fr is given byFr = Fm + 2Fmcos(60)

2 directedalong ‘b’ axis

When a poly phase current flow in a balanced poly phase circuit, arotating magnetic field of constant magnitude is created and thespeed of rotation is synchronous speed

The effect of polyphase currents in polyphase windings is equivalentto the mechanical rotation of permanent magnets, or dc excited fieldpoles, at synchronous speed.

basic principle

State-3

Ia = −Im/2; Ib = Im; Ic = −Im/2The resultant mmf Fr is given byFr = Fm + 2Fmcos(60)

2 directedalong ‘b’ axis

The effect of polyphase currents in polyphase windings is equivalentto the mechanical rotation of permanent magnets, or dc excited fieldpoles, at synchronous speed.

basic principle

Production of RMF- Space Phasor MMF

basic principle

Rotating flux in a polyphase machine

Synchronous speed(Ns) is given by Ns = 120fP , where Ns in rpm.

Stator mmf is assumed to be sinusoidally distributed in space ie.,along the air gap periphery

The stator mmf and rotor mmf produce set of pole pairs which eithertend to attract or repel each other

This attraction or repulsion results in development of electromagnetictorque

Electromagnetic torque is proportional to product of interactingmagnetic fields and sine of electrical space angle between theirmagnetic axes.

basic principle

The electromagnetic torque is given by Te = −π8P

2φFr sinδr and isnegative because, it acts to reduce the space angle betweeninteracting fields.

Also, δr is not time varying and is considered to be cosntant.

basic principle

The electromagnetic torque is given by Te = −π8P

2φFr sinδr and isnegative because, it acts to reduce the space angle betweeninteracting fields.

Also, δr is not time varying and is considered to be cosntant.

Induction Motor

Polyphase Induction motor

Induction motor operated on principle of induction just like atransformer

Stator winding is distributed while rotor can be either squirrel cage orslip ring

The stator of a poly phase induction motor may be considered likeprimary of a transformer

Squirell cage rotor:

Uninsulated conducting bars are embedded in the rotor slots and theirends are short-circuited with rings made of same material asconducting barsThe transformer windings are concentrated while in induction machinesthey are distributed

Induction Motor

Uninsulated conducting bars are embedded in the rotor slots and theirends are short-circuited with rings made of same material asconducting bars

The transformer windings are concentrated while in induction machinesthey are distributed

Induction Motor

Polyphase Induction Motor

No load current in induction motor varies between 30 to 50% while intransformer it is 2− 6% of full load current.

Starting current is 6 times of full load current.

The rotor mmf is also termed as armature mmf as in the case ofinduction motor, stator and rotor windings are called as field andarmature windings.

A squirell cage motor can adjust to any number of poles while in thecase of slip ring induction motor, the number of stator poles shall beequal to rotor poles.

The end of windings in the case of slip ring induction motor arebrought onto the rotor shaft and connected to slip rings.

The rotating magnetic field wave travels at synchronous speed withfrequency of supply .

Induction Motor

The rotor runs at a speed less than synchronous speed and hencemachines is also called as asynchronous machine

The relative speed between rotor and rotating mmf wave is (ω − ωr )if the rotor is rotating in the direction of the rotating mmf waveotherwise it is (ω + ωr )

This relative velocity induces emf in the rotor coil of ‘n’ turns, givenby e = n(ω − ωr )φsin(ω − ωr )t

The difference between rotating mmf wave and rotor speed is calledas slip speed and is given by: (ω − ωr ).

Slip is defined as ration of relative speed to synchronous speed,s = (Ns−Nr )

Induction Motor

Rotor rotating in opposite direction to rotating mmf.

The relative speed is (ω+ωr ), the frequency of generated emf is (2-s)f.A poly phase induction motor with slip-ring or wound-rotor type can beused as frequency converter

Speed of rotor field wrt stator structure = mechanical speed of therotor + speed of the rotor field wrt rotor structure

The relative speed between the stator mmf and rotor mmf is zero andhence both mmf are stationary with respect to each other resulting insteady torque

Induction Motor

The relative speed is (ω+ωr ), the frequency of generated emf is (2-s)f.

A poly phase induction motor with slip-ring or wound-rotor type can beused as frequency converter

Induction Motor

In case of rotor of induction motor attains synchronous speed, theemf inducted in the rotor is zero and hence no rotor mmf and hencezero torque.

For any value of slip (s), the induced emf in the rotor circuit is givenby sE2.

The rotor leakage reactance at stand still, x2 = 2πf1l2 and at any slipis given by 2πf2l2=sx2

Induction Motor

Rotor current is given by I2 = sE2√r22+(sx2)2

= E2√(r2s)2+x22

Rotor current lags the voltage by θ = tan−1 sx2r2

Per phase input power to the rotor circuit is given by Pg = I 22r2s . Pg

is also the air gap power transferred from stator to the rotor circuit.

Air gap power = rotor ohmic losses + internal mechanical powerdeveloped

Induction Motor

= E2√(r2s)2+x22

Induction Motor

= E2√(r2s)2+x22

Induction Motor

= E2√(r2s)2+x22

Induction Motor

Air gap power (I 22r2s ) = rotor ohmic losses (I 22 r2)+ internal

mechanical power developed I 22 r2(1−ss ), ∴

I 22r2s

= I 22 r2 + I 22 r2(1− s

Internal mechanical power developed is given by Pm = (1− s)Pg .

Induction Motor

I 22r2s

= I 22 r2 + I 22 r2(1− s

Induction Motor

I 22r2s

= I 22 r2 + I 22 r2(1− s

EN 206 - Power Electronics and Machines

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